Fix \(\ell \)  and a set of indices \(K\) . The space \(_K^\ell \)  has a comeagre subset \(_{K,*}^{\ell ,\mathrm {reg}}\subset _{*,K}^\ell \)  whose elements \(Y\)  are defined by the condition that all simple \(J_Y\) -spheres \(u\colon P̏^1\rightarrow V_K\) , not contained in \(V^K\cap V_K\) , are regular (standard adaptation of the argument of [1]}).
